| 173 | == Additional routines for 3D-Var == |

| 174 | |

| 175 | For the 3D-Var methods added with PDAF V2.0 two more routines are required in the observation module. |

| 176 | |

| 177 | === `obs_op_lin_TYPE` === |

| 178 | |

| 179 | This routine applies the linearized observation operator to a state vector. It returns the observed state vector to PDAF. The routine is used only by the 3D-Var methods. |

| 180 | |

| 181 | '''Note:''' A separate routine for `obs_op_lin_TYPE` is only required if the full observation operator in `obs_op_TYPE` is nonlinear. If `obs_op_TYPE` is linear, one can just insert calls to this operator in the routine `obs_op_lin_pdafomi` in `callback_obs_pdafomi.F90`. |

| 182 | |

| 183 | PDAF-OMI provides several linear observation operators. For example the observation operator for observations that are grid point values is called as: |

| 184 | {{{ |

| 185 | CALL PDAFomi_obs_op_gridpoint(thisobs, state_p, ostate) |

| 186 | }}} |

| 187 | |

| 188 | Here, `state_p` is the state vector and `ostate` is the observed state vector. |

| 189 | |

| 190 | For more information on the available observation operators and on how to implement your own observation operator see the [wiki:OMI_observation_operators documentation of observation operators for OMI]. |

| 191 | |

| 192 | === `obs_op_adj_TYPE` === |

| 193 | |

| 194 | This routine applies the adjoint observation operator to an observation vector. It returns the state vector to PDAF. The routine is used only by the 3D-Var methods. |

| 195 | |

| 196 | PDAF-OMI provides consistent pairs of linear observation operators. For example the adjoint observation operator for observations that are grid point values is called as: |

| 197 | {{{ |

| 198 | CALL PDAFomi_obs_op_adj_gridpoint(thisobs, ostate, state_p) |

| 199 | }}} |

| 200 | |

| 201 | Here, `ostate` is the observation vector and `state_p` is the state vector. |

| 202 | |

| 203 | For more information on the available observation operators and on how to implement your own observation operator see the [wiki:OMI_observation_operators documentation of observation operators for OMI]. |

| 204 | |

| 205 | |